{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import packages/modules\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import integrate\n",
    "from scipy.stats import uniform\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import rv_continuous\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# define functions\n",
    "def epstar1(cost1,beta,uncond_vote2,exp_eps2,cost2):\n",
    "    return cost1 + beta*uncond_vote2*(exp_eps2 - cost2) \n",
    "\n",
    "def cdf(z):\n",
    "    return integrate.quad(lambda x: uniform.pdf(x), 0, z)[0]\n",
    "def cond_exp(z):\n",
    "    return rv_continuous.expect(uniform, lb=z, ub=1, conditional=True)\n",
    "\n",
    "def cdf_n(z):\n",
    "    return integrate.quad(lambda x: norm.pdf(x), -np.inf, z)[0]\n",
    "def cond_exp_n(z):\n",
    "    return rv_continuous.expect(norm, lb=z, ub=np.inf, conditional=True)\n",
    "\n",
    "# vectorize\n",
    "cdf_vec = np.vectorize(cdf)\n",
    "cond_exp_vec = np.vectorize(cond_exp)\n",
    "\n",
    "cdf_n_vec = np.vectorize(cdf_n)\n",
    "cond_exp_n_vec = np.vectorize(cond_exp_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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o9UUvht00jHrX1nM2MKW8SMuW/76vWzc7Bf78eVvG50p9+tjj2DG4445/PrZ0aebndLXM+KpVq4iIiKBUqVIMGzaMmjVrZv7mXsCdYxSlgX2pbu9Pui+1D4DqwAFgK/CIMf/uhBeRfiKyXkTWHz161F3x/kvLlnZtxdat8NRTHjutS3af3M32Y9tpMKEBz33/HBcuXXA6JKUClitlxuvVq8eePXvYvHkzgwYN4tZbb/VQdFfPnS2KtKooXXk12wGbgNbAdcB3IrLcGHP6Hy8yZjwwHiAqKsqjc0U7dIBvvoGoKE+eNXONyjYidkAsT333FG+ufJM5v8xhUudJNC3X1OnQlHJURi2AvHkzfrxYMddaEFdypcx46uJ/HTp0YMCAARw7doxixYpl/YQe5s4WxX6gbKrbZbAth9T6AnOMtRPYDVRzY0zZctNNdvrsxYvwzjsQ7xWdY1A4T2Emdp7Id72/Iy4hjmZTmvHwgoc58/cZp0NTKqC4Umb80KFDl1sea9euJTExkaJFfWNSijsTxTqgsohUTBqg7gHMveI5e4E2ACJSEqgK/O7GmK7K/Pnw9NPQty8kJDgdTYobK91IzEMxPNrwUcasG0OtD2uxcOdCp8NSKmCkLjNevXp1unXrdrnMeHKp8dmzZ1OrVi0iIiIYPHgwM2bM8Jld8MSdq35FpAPwHnZ67GRjzGsi0h/AGDNWREoBHwHXYruq3jTGfJLRe0ZFRZn169e7LebMvP46DBliB74mTYIgL1uJsmrfKu6fez87ju9g1+BdlC9U3umQlMrQ9u3bqV69utNh+JW0rqmIbDDGZKsT3a3rKIwxC4AFV9w3NtXvBwCfqq393/9CXBy89BKEhMC4cd6VLBqVbcTP//mZZXuWXU4S6w+sp/619X3m24tSyrt40Uec7xg61LYq5syBvV64s2mukFy0va4tACv2riB6QjQfb/nY4aiUUr5KE0U2iMArr9hpsxUq2Pu8tW7fDWVuYEyHMdxZ404A/jz9pxYZVEpliSaKbBJJ2RXvpZfgySe9M1mEBIXwUPRD5AnNw7m4czSd0pS2H7fl95NeO2dAKeVlNFFcJWPg+HEYMQKee847k0WyPKF5eKbJM6z9cy21P6zNe6vfIyHRi6ZvKaW8kiaKqyQCI0fCQw/BW2/BCy94b7IIkiD6R/Vn24BttKzQkscWPUbTKU2JPRqb+YuVUgFLE0UOEIEPPoAHH4TXXrPjF96sbMGyfNPzGz7p+gm/Hf+NuuPq8sqPrxCXEOd0aEr5rMzKjJ88eZKuXbtSp04dGjRoQExMjANRZo8mihwSFARjx8IDD6QMcHszEeGuOncROzCW26rfxotLXyR6QjQbD250OjSlfE5ymfFvv/2W2NhYpk+fTmzsP1vqr7/+OpGRkWzZsoVp06bxyCOPOBRt1mmiyEFBQTBhAtxzj739yy/e2w2VrES+Eky/fTpf9/iaY+ePcfDMQadDUsrnuFJmPDY2ljZt2gBQrVo1/vjjDw4fPuxEuFnm1gV3gSwmBurXh8GD4e23bfeUN+tctTNtK7UlT2geAMauH0v1YtVpUaGFw5EplTUtP2qZ6XM6VenEk42fvPz8PpF96BPZh2Pnj3HHzH/WGV/aZ2mm7+dKmfGIiAjmzJlD06ZNWbt2LXv27GH//v2ULFky8z/KYdqicJMaNWw31LBh8Nhj3t+yAC4nibiEOEauGcmEjRMcjkgp3+BKmfFnn32WkydPEhkZyahRo6hbty4hIb7xXd03ovRBQUF2gDs01M6KunQJRo3yrnIf6QkLDmP9g+u5lHgJgJgjMez5aw8dq3R0ODKlMudKCyC95xfLWyzLrwfXy4xPmWJ3ejbGULFiRSpWrJjlcznBBz62fJcIvPuuXYw3Zgx8/rnTEbkuX1g+CuUuBMDbK9+m0/RO3D3nbo6d95J9YZXyIq6UGf/rr7+Ii7MzCydOnEjz5s3/sUeFN9MWhZuJ2DGKxo2hSxeno8meiZ0nUqlwJV5f/jqLdi1iVPtRdK/ZXYsMKpUkdZnxhIQE7rvvvstlxgH69+/P9u3bueeeewgODqZGjRpMmjTJ4ahd59Yy4+7gdJnxq7V7N4webRfnBQc7HU3WbD28lfvn3s+6A+voXLUzYzqMoXSBK3e3VSprtMx4zsvpMuPa9eRh8+fD8OHQq5ctV+5Lapeszar7VzH8puF8t+s7aoypwYQNE7TIoFJ+Lt1EISLBIvIfEXlFRJpc8djz7g/NPz38sN1OdeZM6NoVLlxwOqKsCQ4K5vFGj7P1oa3Uv7Y+/b7px20zb3M6LKWUG2XUohgHtACOA++LyIhUj+knw1V48km74dG338LNN8Pp005HlHXXFbmOH+75gfGdxnNr1VsBO5NDiwyq7NBWac5xx7XMKFE0MMb0Msa8BzQEwkVkjojkwm5bqq5Cv37w6acQH+/9i/HSIyI8WP9B7o28F4DJP0+m8eTGOjNKZUnu3Lk5fvy4JoscYIzh+PHj5M6dO0ffN6NZT2GpTh4P9BORF4HFQHiORhGgevaE7t3t2opz5+DMGbjmGqejyr5CuQtRrmA5iuQp4nQoyoeUKVOG/fv3c/ToUadD8Qu5c+emTJkyOfqe6c56EpFPgE+MMQuvuP8B4ENjTGiORuIiX5/1lJ7bb4fNm+H7732jqGBmDpw5QPfZ3Rl+03AalG7gdDhKBTy3zHoyxtx9ZZJIun+iU0nCnz39NJw4AU2b2mKCvm7fqX388dcfNJrUiCcWPcH5S+edDkkplU06PdZLNGwIS5faMYtmzWCjj1f7blimIdsGbKNfvX6MWD2C2h/WZsnuJU6HpZTKBk0UXqROHVi+HPLmtessEnx8AlGBXAX4sNOHLL13KUESROtprek3rx+nLp5yOjSlVBZoovAylSvDihUwa5bvrdxOT4sKLdjcfzNPNX6KST9PosaYGsz7dZ7TYSmlXJTRYHa9jF5ojHGkc8RfB7PT8+yzdnC7f3+nI8kZ6w+s576v7yP2aCw7B++kQqEKToekVEC4msHsjKbHDk/6mRuIAjZj10/UAdYATbNzQuW6S5fsBkhvvQWHDsHQob675iJZVKko1vdbz8q9Ky8niVX7VnFDmRu0yKBSXiqjWU+tjDGtgD1APWNMlDGmPlAX2OmpAANZaCh8+SX06QMvvQQDBvj+uAXY/S5aVWwFwIq9K2g8uTHTNk9zOCqlVHpcKTNezRizNfmGMSZGRCLdF5JKLTQUJk+GkiVty+LUKfjsM6ejyjmNyjRiwi0T6F6rO2Cn1ZYuUJog0eEzpbyFK4liu4hMBD4BDHA3sN2tUal/EIE337Srtkv7WVXv4KBgHqj3AADn4s7RbEozyhcqz8RbJlK5aGWHo1NKgWuznvoC24BHgEeB2KT7lIc9+ijceaf9/Ztv4MABR8PJcXlD8/JiixfZfGgzdcbW4e2VbxOfGO90WEoFPJc2LhKRMKAqtkXxqzHmkrsDS0+gzXpKy6lTUKkS5MsHCxZArVpOR5SzDpw5wID5A/j616+pf219JnWeRMQ1EU6HpZRPc+vGRSLSEvgN+AAYA+wQkebZOZnKGQULwg8/2IHtJk3s7/6kVP5SfNn9S2beMZN9p/cRNSGKFxa/wN/xfzsdmlIByZWup+HATcaYFsaY5kA74F33hqUyExkJq1dDuXJ2T4upU52OKGeJCHfWvJPYAbH0rNWTV5e/St1xdVn751qnQ1Mq4LiSKEKNMb8m3zDG7AC0KKAXKFvWruJu2RJ27HA6Gvcomrco07pOY0GvBZyNO8uJCyecDkmpgJPpGIWITMaOTXycdNddQIgxJtMBbRG5GRgJBAMTjTFvpvGclsB72ORzzBjTIqP31DGKf7t0CUJC7OyoX3+FihUhLCzz1/mai/EXyR1iN2T5YO0HVCtWjRsr3ehwVEr5BreOUQAPYWc9DcbOfIoFMi0oISLBwGigPVAD6CkiNa54TiHsuEdnY0xN4M6sBK+s0FCbJE6dgubNoX17+7u/SU4SlxIuMXb9WKZu9rP+NqW8VKbrKIwxfwMjko6saADsNMb8DiAiM4Au2ESTrBcwxxizN+lcR7J4DpVKwYLwzjtw//12kHvBAjuG4W9Cg0NZ9+A64hLiANh6eCs7T+yka/WuDkemlH9Kt0UhIjOTfm4VkS1XHi68d2lgX6rb+5PuS60KUFhElorIBhG5J51Y+onIehFZr9slZuyee2DRIti/Hxo0sAPe/ihPaB4K5i4IwPBVw7lt5m10m9WNw2cPOxyZUv4no66nR5J+dgJuSePITFoV3q4cEAkB6gMdsbOpXhCRKv96kTHjk2pNRRUvXtyFUwe21q3hp5/sOov33nM6GvebcMsEXmv9Gl//+jXVR1dn2uZpuLI+SCnlmoyKAh5MGmeYZIzZc+XhwnvvB8qmul0GuHIt8X5goTHmnDHmGLAM0JVVOaBGDVizBiZOtLdPnoTERGdjcpfQ4FD+2+y/bO6/merFq3PvV/fS4bMO7D211+nQlPILGQ5mG2MSgPMiUjAb770OqCwiFZNWdvcA5l7xnK+BZiISIiJ5gYZoHakcU6wYhIfDxYu2ldGjB5z3462rqxWrxvK+y3n/5vdZvmc5NcfUZPTa0SQaP82QSnmIK7OeLgJbRWSSiLyffGT2ImNMPPAwsAj74T/TGLNNRPqLSP+k52wHFgJbgLXYKbQx2f1jVNpy5YK774bZs+2sqD//dDoi9wmSIAY1HETMgBgalWnEw98+TJcZXbQrSqmr4Mo6invTut8Y48jcRF1HkX3z5tm9uAsUgLlzoX59pyNyL2MM0zZPI0iC6B3RG2MMCSaBkCBXiiYr5V+uZh2Fq0UB8wDlUq/QdoomiquzZQvccostWb56te/vmJcVEzZMYOyGsSy8ayHF8+mkCBVY3F0U8BZgE7aLCBGJFJErxxqUj6hTB9auhZkzbZK4eNF/B7mvVCJfCaoUrUKxvMUAtDtKKRe5MkbxP+ziub8AjDGbgIpui0i5XcmSUL48GGPXXXTp4p8rua/UpVoXpt8+HRHhz9N/0mhSI1buXel0WEp5PVcSRbwx5sqPEf0q5idatICFC6FhQ/jlF6ej8ZyDZw9y6Owhmk1pxqAFgzjz9xmnQ1LKa7mSKGJEpBcQLCKVRWQU8JOb40rfgQP2q7C6aiIwcKDdz+LECbuSe26AdCpGlYoiZkAMDzd4mNHrRlPrw1os2rnI6bCU8kquJIpBQE3gb2A6cBq7JaozDh6EBx+EeN0iM6c0bw4bNkCVKrZO1JkA+XIdHhbO++3fZ3nf5eQJycPNn95Mn6/6aClzpa7g0qwnABEpABhjjKMfI1GlSpn1Bw9C167w2WeQO7eT4fiVCxfgt9/sgHdior2dL5/TUXnGxfiLvLrsVd5c8SbF8hZjdIfR3F7jdqfDUirHuHvWU7SIbMUuitsqIptFxLkZ+KVKwciR8OWX0KEDnD7tWCj+Jk8emyQA3ngDoqP9d0OkK+UOyc2rrV9lfb/1lMpfih5f9GD3yd1Oh6WUV3Cl62kSMMAYU8EYUwEYCExxa1SZGTwYPvkEli+3tSm0omyOa9zYXtboaJgzx+loPCfymkjWPriWxfcspmJhO7lv2Z5lOpVWBTRXEsUZY8zy5BvGmBWA873Yd90FX30F27ZB06awVwvA5aRWrey4RbVqcPvt8OSTdie9QBASFEKz8s0AWLF3BS0+asFHmz5yNiilHORKolgrIuNEpKWItBCRMcBSEaknIvXcHWCGOnaE776Dw4ftTj3btZ5gTipXDpYtszOjRo60q7oDTeOyjfmoy0f0qt0LgD/++kOLDKqA40qtpyUZPGyMMa1zNqSMpVnCY8sWaNfOfuVdsMDO81Q5ascOOysK4I8/oEIFJ6Nxxrm4c1QfXZ1yBcsxsfNEqhWr5nRISrnMrYPZxphWGRweTRLpqlMHVqywe4G2agXffON0RH4nOUksWgSVK8NbbwXecpa8oXl5tfWrbD+2nYixEby+/HUuJQRIf5wKaK50PfmG666z27pVr25rUowb53REfqlxY7jtNnj2WTtD+a+/nI7Ic0SEeyLuIXZALF2qdmHI4iFET4hm48GNToemlFv5T6IAW8Ro6VK4+Wbo3x+GDAm8r71ulj8/zJhht1idPx+iouDnn52OyrNKhpdk5p0zmdNtDofPHabBhAY8+/2zXLh0wenQlHIL/0oUYLd0+/pru3r79dfh3nshLs7pqPyKCDzyCPz4o60+u26d0xE5o2v1rsQOiKVPZB/eWvkWEWMj+Gmfc9VtlHIXl3ZwEZHGQIXUzzfGTHNTTFcvJMR2PZUrBy+8YOtDffGFHcNQOaZxY4iNta0MgCVLICICihRxNi5PKpynMBM7T6RHrR70m9ePs3FnnQ5JqRznyqynj4HrsHtSJCTdbYwxg90bWtqyvHHR1KnwwANQo4adEVW6tPuCC2BnztjS5fnzw/TpNokEmriEOMKCwwB4b/V7VC1alfaV2zsclVKWW2c9AVFAE2PMAGPMoKTDkSSRLffeaxPE7t1www2BuRjAA/Lnh//7P9uYa94c3nwzcDZESpacJC4lXOKjTR8xY9sMhyNSKme4VGYcuMbdgbhV27Z25Vhiol2YN3++0xH5pago2LjRruR+7jk7pyAQh4dCg0NZ88AaRrUfBcDmQ5uZtW2WlgFRPsuVRFEMiBWRRSIyN/lwd2A5LjLS7gFapQp07myXGus/3BxXsKCdFTVuHNSqBWFhTkfkjFwhuSiQqwAAI9eMpNvsbrSZ1oa1f651ODKlss6VMYoWad1vjPnRLRFlIstjFFc6dw5697bVZ/v3h/ffh9DQnAtQ/cv69TBrFrz8MuTK5XQ0nhefGM+7q97ljRVvcDbuLO+2e5cB0QMQEadDUwHE3Suzf0zryM7JvEK+fDB7tl0xNnasLVUeSKvGHLBoEbz9th0iCsRyXCFBITzV5Cl2Dt5J2+va8vC3D3PXnLt0hpTyGekmChFZkfTzjIicTnWcERHf3gQiKMhuuDBlil0M0KgR7NrldFR+a8gQu7Rl/36oVw9Gjw7MXr8ieYowr+c8Xm31KjNiZtBwYkN+ORZAG5Urn5VuojDGNE36md8YUyDVkd8YU8BzIbpRnz7w/fdw5Ag0bGgHvJVbdO4MW7dCy5bw8MN2O5FAFCRBDGk+hP/r/X8cPXeU6AnRfBH7hdNhKZUh/1uZnVXNm8OaNVCsGNx4I4wf73REfuuaa+xM5c8+g5497X0nAnR76hsr3cjG/2ykTsk6hAbrGJnybpooAK6/HlavhjZt4D//sYPcgTiv0wNEbJIICYFjx+zMqIcegvPnnY7M88oUKMPyvsvpXLUzAJ/HfM7+0/sdjkqpf9NEkaxQIVue/Nln7dzO1q3h0CGno/Jr+fPbjQrHjrVjF2sDcOZokNh/gqcunuKh+Q8xdMlQhyNS6t8yTRQi8pYr9/mF4GA7yP3557YkalRU4Fa884BcueCdd+ww0blzdk7BkCGQkJD5a/1NwdwFWXX/Kka0GwHA8fPHdSc95TVcaVG0TeM+/y5g062b3dsiNBSaNYNp3lv/0B+0aQMxMbbaytatdlJaIKparCoFcxckLiGOmz65ifaftufIuSNOh6VUhtNjHxKRrUBVEdmS6tgN+H/BpIgI25po0sR+gj36KMTHOx2V3ypYECZPtktcROD33+G11+zutoEmNCiU/9T/D8v2LCNibARLdme0G7FS7pfRd7fPgFuAuUk/k4/6xpi7PRCb84oVs6vFHn3Ulvxo2xYOH3Y6Kr+WXPJj1ix4/nnbHbVtm7MxeZqI0K9+P9Y8sIaCuQpy48c38tLSl0hIDMA+OeUVMlpHccoY8wfwDGBSHeEiUs4z4XmBkBB4913b/bRmDdSta/fnVm71zDO2dbFnjx3ofuedwBu7qFOyDuv7reeu2nfxvx//x02f3MTBMwedDksFIFd6g+cD3yT9/AH4HfjWnUF5pd69baIID7erxoYPD8zlxR50++22NdGxIzz9NIwY4XREnhceFs7UW6cyufNkVu1bReS4SL7b9Z3TYakA40qtp9rGmDpJPysDDYDA/Epdu7Ydt+jSBZ58Eu64A06dcjoqv1aihN2ccOZMu94CbCsjkMYuRIS+dfuyvt96iuctTrtP2rF6/2qnw1IBJMvzS4wxG4FoV54rIjeLyK8islNEns3gedEikiAid2Q1Ho8rWND2iQwfbgsYRUXpZkhuJgJ33mkbc5cuQfv2EB0NGzY4HZln1Sheg7UPrmV0h9E0LN0QsJVplXI3V9ZRPJ7qeFJEPgOOuvC6YGA0diptDaCniNRI53lvAYuyHL1TRODxx2HpUrsA4IYb7Jaryu1CQ+H111PKcz3zDFy44HRUnpM3NC8PRT+EiLDrxC6qflCVZXu0RplyL1daFPlTHbmwYxVdXHhdA2CnMeZ3Y0wcMCOd1w0CvgB8b8J406Z2Yd4NN9gCg/ffbxOHcqtbb4XYWOjb15Yvr1MH/vjD6ag8z2AoX7A85QuWdzoU5edcGaN4yRjzEjACGGmM+dQYc9GF9y4N7Et1e3/SfZeJSGmgKzA2ozcSkX4isl5E1h89mmljxrNKlrSbRQ8ZYsuWa1eURxQqBBMmwA8/2M0Ly5Sx9wfS/ILri1zP4nsXU75QeYwxPLHoCS1brtzCla6nWiLyM3bv7G0iskFEarnw3mlt33XlP+P3gGeMMRlOfDTGjDfGRBljoooXL+7CqT0sJARefRW++85ugtSgAYwZE1ifWg5p3dquuQgJgePHbZ7+8svAu/S7/9rNtC3TqD++PhM3TtT9uVWOcqXraTzwuDGmvDGmPPBE0n2Z2Q+UTXW7DHDgiudEATNE5A/gDmCMiNzqwnt7pzZtYPNmaNUKBg608ztPnnQ6qoBx7JhdPH/bbXZi2p49TkfkOZUKV2Jz/800LtuYB+c9SLfZ3Th5Qf/fUznDlUSRzxhzuYaAMWYpkM+F160DKotIRREJA3pgV3lfZoypaIypYIypAMwGBhhjvnIxdu9UogTMn29XiM2bZ/tFVq50OqqAULWqnQk1bBgsXgw1atgxjMQAqa1XKn8pFt29iLdvfJuvfvmKiLERLN+z3OmwlB9wJVH8LiIviEiFpON5YHdmLzLGxAMPY2czbQdmGmO2iUh/Eel/dWF7uaAgu85i5UpbkbZFC1u4KNCWFjsgJASeeMIOdrdta2s7BlKRwSAJ4qkmT7Hq/lXkDslNy6kteXHJizqNVl0VyawvU0QKAy8BTbHjDsuA/xljHGnXRkVFmfXr1ztx6uw5dcpuhvT55ymVaCtUcDqqgHHhAuTJAzt32pbGa69B0aJOR+UZZ+POMvjbwUzZNIVGZRrxdY+vKZ7PC8f4lEeIyAZjTFR2XuvKrKeTxpjBxph6xpi6xphHnEoSPqlgQZg+HT76CDZtsnM5p04NvNFWh+TJY38uWwYTJ0K1aoFz+cPDwpncZTLTb59O/lz5KZS7kNMhKR/lyqynKiIyXkT+T0QWJx+eCM5viNhS5Zs32/LlffrYpcbHjzsdWcC47z7YuBEqV7aXv0WLwJnF3KNWDxbetZDQ4FCOnz/O4G8Hc+qilp5RrnOl93YW8DPwPPBUqkNlVcWKdjX3G2/A3Lm2dtQi31mQ7uvq1LGFf8ePt2MYU6Y4HZHniNjZ6kv+WMLEjRPZ/Vemw4xKXebKGMUGY0x9D8WTKZ8bo0jPzz/bDaO3b4dBg+Ctt1L6SZTbnThhB74LFIDly+GXX2yrIzjY6cjc78i5I5TIVwKAWdtm0blqZ3KF5HI4KuVubh2jAOaJyAARuVZEiiQf2TmZSqVuXTuX85FHYNQoe3u1VgT1lCJFbJIAO7+gXz9bOyoQ/hMkJ4nNhzbTbXY3oidEs/XwVoejUt7MlURxL7ar6SdgQ9LhB1/pvUCePPDee3ZF9/nzdtvVp58OrCp3XmD8ePj0UzhwwO6o17dvYGxkGHFNBN/0/IbD5w4TNSGK4T8NJ9EEyKITlSUZJgoRCQKeTVoYl/qo5KH4AsONN0JMDDzwgF2op60LjxKBXr3g119tnv70U7v/RSDoWKUjMQ/F0P769jz53ZO0mdaGvaf2Oh2W8jIZJgpjTCIw0EOxBLYCBWDcOFtgMLl18dRT2rrwoPz57VDRtm0pmyTNmWO3HfHn6bTF8xXny+5fMqnzJNYfWE+dD+vw6ZZPtV6UusyVrqfvkvahKKtjFB7Qtm1K62LYMNu6WLXK6agCSuXKdqAb4IMPbFnzNm3sMhh/JSLcV/c+NvffTM0SNbn7y7vp8UUP/rr4l9OhKS/gSqK4D9uqWIaOUXhGcuviu+9si6JJE3jsMTh71unIAs6iRTB6tF1zUa+e3XLk4EGno3KfSoUrsazPMl5r/RpbDm8hWAJgGpjKVKbTY72N30yPddXp03Ybt7FjoVw5W768Y0enowo4f/1ly3+MHGnLmAfCf4K4hDjCgsO4cOkCb654kycbP0n+XPmdDktlk1unx4rIPWkd2TmZyoYCBeDDD+1KsfBw6NQJuneHQ4ecjiygFCpk5xn8/jt06GDve+89+OQT/61OGxYcBsAPu3/g1eWvsu7AOocjUk5xpespOtXRDPgf0NmNMam0NGliF+m98gp89ZUtWjR+vP9+SnmpMmXsLKnERDvQ3bu33afqhx+cjsx9OlXpxG+DfqN1xdYAzN8xn/OXzjsclfIkV4oCDkp1PAjUBcLcH5r6l7AweP5522EeGWmr0rZoYVd3K48KCrLVWKZNg6NH7Qzndu3sCm9/VKmwnRG/79Q+bv38ViLHRvLTvp8cjkp5SnYq9Z8HKud0ICoLqlaFJUtg0iQ7lzMiAl54wU6rVR4TFGRbFL/+CsOH26KDly7Zx3xs6M9lZQuW5f/u/j/iEuJoNqUZT3/3NBfjLzodlnIzV2o9zSNlr+sgoAYwyxjzjJtjS1PADWZn5sgRePxxu0qsfHnbcd6li+0fUR518SLkzm1/v/deO67x/PPgjdu8X60zf5/hif97ggkbJ1CjeA2m3jqVqFLZGidVHuLuWk/DgOFJxxtAc6eShEpDiRJ2RHXpUrtirGtXO9r6229ORxZwkpNEYqKtzjJ6NFSqBC+/7H8zm/Pnys/4W8bz7V3fcuriKW6YeAMvLH6BuIQ4p0NTbuBKouhgjPkx6VhpjNkvIm+5PTKVNS1a2L6Pd9+1W7DWqgVDhsC5c05HFnCCguxs5pgYuOkmGDoUrrvObp7kb26+/mZiBsRwV527eHX5qzSY0IAdx3c4HZbKYa4kirZp3Nc+pwNROSA0FB591Haad+sGr78O1avb6Tn+2mnuxapVgy++sAvr69e3Q0sA+/dDnB998S6UuxBTb53KV92/4lLiJQrkKuB0SCqHpZsoROQhEdkKVBWRLamO3UCA7A3mo669Fj7+2H6FLVQIbr/dlgYJlC3dvMwNN8CCBVCypM3X3brZJPLRRxAf73R0OadLtS5sfWgr14RfQ6JJ5MG5D7L+gI4n+oOMWhSfAbcAc5N+Jh/1jTF3eyA2dbWaNbPdUe+/b3/WrWun1AZCDW0v9sILdj+Mvn2hZk27pbq/LIcJEvuRsuevPSzYuYBtR7Y5HJHKCVrCI1CcOGFHVUePtiOt//2v7aZKHoFVHmWMrUr74ouwdStMnGjrSPmTM3+fITwsHBFhRswMyhQoQ9NyTZ0OK2C5e9aT8gdFitipszEx0LIlPPecHb+YOVPHLxwgYqvSbtoEs2bZ/TAAvvnGbqfuD/9J8ufKj4iQkJjAa8tfo/mU5gz+djBn4/xsClgA0EQRaKpWtZ9E339v60h17267qNascTqygBQUBHfckbJd+siRdhlM3bowe7Z/dEkFBwWz6v5VDIweyKi1o6j9YW1++N2Pa574IU0UgapNGztuMWEC7NxpR1xvv91/a1D4iG+/tWVBLlyAO++EOnVsqXNfFx4WzqgOo1jWZxmhQaHc+PGN9JvXj1MXTzkdmnKBJopAFhxsN0j67Tf43//s7no1a8KDD9o5nMrjQkJsWZDYWDvIbQycOWMfu3DB92dJNSvfjM39N/NU46eY9PMkao6pyfwd850OS2VCE4WyK7qHDrU1tAcNgqlT7TZvTz9tB8GVxwUHQ48edqD7ttvsfW+/bXsOJ0707XUYeULz8Hbbt1l9/2oK5S5Ep+mdeGP5G06HpTKgiUKlKF7cDnjv2GH7PYYNs0uK33xTCw46JCjIHmB7B4sUsQ2+ypXtBDZf3lI9unQ0G/ptYGiLodxa7VYALly6oHt1eyGdHqvSt2WLnUY7fz5ccw08+yz065cy8qo8zhhYuNBuS7JqlZ0t9emnTkeVc3rM7sHF+It82f1LRAtb5iidHqvco04dO19z2TK7lPjRR20LY9QoWypVeZwItG9vy3ktXWp7BwF27YInn4Q//3Q0vKtijKFJ2SY0K9fscpJINH4w7csPaKJQmWvWzO5/sWSJ7fMYPBiuv97u3/33305HF5BEbB3IiAh7e9ky22tYsaJduOeLk9dEhEENB/FE4ycA+PqXr2kwoQGbDm1yNjCliUJlQcuW9mvs999DhQowcKBNHGPH+vboqh/o29dOXuvXDz77DGrUgJ49fXvhXpAEsf/0fqLGR/HMd8/o9qsO0kShskbErsFYvtxOpy1TBh56yHZJjRypZc0dVLEifPAB7NljK8wn7+8NsGKF7y3eu6XqLWwfuJ2+kX15+6e3qf1hbb7//XunwwpImihU9ojYirQrV9rR1UqV7BhGhQrw6qtw8qTTEQasEiXsYPc779jb69bZ3sMaNWDcON+awFY4T2EmdJ7AknuXECzBtP24Lfd+dS/Hzh9zOrSA4tZEISI3i8ivIrJTRJ5N4/G7UpUv/0lEItwZj3IDEWjXDn780X5tbdjQlkctXx6eeQYOHXI6woAXGWlnRoWHQ//+UK6c3aL1lA8tim5ZoSVbHtrCkGZD+GzrZ1QfXZ1Pt3yqU2k9xG3TY0UkGNiB3fhoP7AO6GmMiU31nMbAdmPMSRFpD/zPGNMwo/fV6bE+YPNmu/Zi5ky7mdJ998FTT9m+EeUYY2wuHzHC9hz+8YdNHmfO2DWXvmLr4a08OO9Bjp0/RsyAGHKHaAVkV3jr9NgGwE5jzO/GmDhgBtAl9ROMMT8ZY5L7KFYDZdwYj/KUiAhbf+KXX2w9iokT7aB39+5afNBBIrYL6ssv7XTa8HA7btGwIdx4o91cyRfGMWqXrM3K+1ay+N7F5A7JzflL5xm1ZhSXEi45HZrfcmeiKA3sS3V7f9J96bkf+DatB0Skn4isF5H1R48ezcEQlVtVrmyLDu7eDY8/bqvb3XADNGli9whNSHA6woBVsKD9GR8P995rc3rHjrbU14cfwlkvrwQeHBRMuYLlAPgi9gsGLxysu+m5kTsTRVrLKtPs5xKRVthE8UxajxtjxhtjoowxUcWLF8/BEJVHlC5tCxXt22d32zt0yNbWrlzZzpRKrnqnPC4szA4l7d5txzHy5YMBA+xifPCN6bW9I3rz839+plHZRgB8HvM5x88fdzgq/+LORLEfKJvqdhngwJVPEpE6wESgizFG/+v6s/z5bdHBHTtgzhybQB591M7jfOop22muHBEaasuBrFtnS4MkFyJ84w27Etzbu6Uir4kE4PDZw9z71b1U/aAqH236SAe7c4g7E8U6oLKIVBSRMKAHdv/ty0SkHDAH6G2M2eHGWJQ3CQ6Grl3tiOqaNdChA7z7rp1i27mznW7rzZ9KfkzE9g6GhtrbBQvauQkdO0KVKnYg3JtnPpcML8m6B9dRtVhV+n7dl1ZTW7H96Hanw/J5bksUxph44GFgEbAdmGmM2SYi/UWkf9LTXgSKAmNEZJOIaCdjoGnQwA58795tV4mtXWu/wlataj+VtMy5owYOtA29GTNsXcgnnvD+vb1rl6zN8r7LGd9pPFsObyFibATPL36eC5d8uNSuw7R6rPIucXF2oHvMGDuXM3du2ycycCDUq+d0dAHv559t2fOICJvb77/flg3p2hVy5XI6un87cu4IT/7fk3y85WMqFa7EmA5jaHd9O6fDcoS3To9VKuvCwmyRouXLYdMmuOce+3W2fn07j3PCBB38dlDduimFCPfutcmiZ08oW9YOiu/a5Wx8VyqRrwTTuk5j8T2LCQ0K5eZPb2bMujFOh+VztEWhvN+pU3bXvfHjYds2OzWnWze7jWujRikFjZTHJSbakl/jxsG8eXYr18OHU6bfepO/4/9mxKoR3F/vfkrkK8GRc0comqcowUHBTofmEVfTotBEoXyHMXYMY+JE28o4exaqV7cJo3dvu0OfcsyBA3bG1O2329vdutkB8AcftBVdvEmiSaTp5KYUzlOY+b0CY89u7XpSgUEkpfvp4EGYNAkKFbIjrKVL2+1b58+HS7pC1wmlSqUkib//ttu0vvGGrdzSoQPMnWsX+HkDQRjUYBB9I/sCEJ8Yz8kLXjydy2GaKJRvCg+3NaR++sl2Rw0aZPfK6NTJJo1HHrGLAnysxewvcuWyXVG7d9sChJs2QZcuMHmyfdzp/ywiQs/aPbmjxh0AjFk35vLaC91V7980USjfV6MGDB9u9wH9+mu7wdK4cXbqbfXq8NprupjPIeXKwcsv2z0y5syx5b7A9h7eeKPdZOmCF8xabVG+BZWLVqbv131pNqWZ7qp3BU0Uyn+EhdkFezNn2jIhEybYyf/PP2/7P5o3twPix7UAgKeFhtoptMmD3GFhdobUXXfZLquBA2HDBufii7gmguV9lzOlyxR+O/4b9cfX55FvH+HURR+qxe5GOpit/N+ePbaQ0ccf2+p3ISF2l75u3eDWW6FIEacjDEiJiba3cNIku3Smbl07GA62lZEnjzNxnbxwkiGLhzB2/VhK5CvBsJuGcVftuxAfn12ns56UcoUxdsXYrFm21fH77zZptG1rk0aXLlC4sNNRBqSTJ+38hBo17GL8ihXtAv3777c5PciBvo8NBzYwYMEA1v65lublm/Nl9y8pksd3v1TorCelXCFiV3e/8Qbs3Anr19vy59u3Q9++ULKkLWo0daqWDvGwwoVtkgA7aa1PH/juO7jpJps0XnzR85sl1i9Vn1X3r2J8p/EUzl2Ywrntlwhf+3KdE7RFoZQxNmkktzT27LGFC5s3t62MLl3sXuDKoy5etFNqJ02C77+3vYaVK9t5CQULOtP4O3jmIG2mtWFMxzG0rNDS8wFcBW1RKHU1RCA62u6ZsXu3XdT37LNw5Igtg16xot14euhQ23XlY1+ufFXu3LZHcNEi25qoXNne/+STdo7CnXfaKbieXDbz18W/KJS7EKXz2z3YfO2LdnZpi0KpjOzcaafcfv01rFxpR2DLlbOzqzp2hBYtnBt1DVA//2x7Bz/7DI4etQvyH3sMnnvO87F0m9WN6wpfx/PNnydfWD7PB5AF2qJQyl2uv96u/F62zH6tnTzZTs+ZNMmOthYpYpcdjxoFv/3mdLQBoW5deO89u2xm3jy7bCZ5+5K4OFud/s8/3R9HXEIc+cLy8ebKN6k+ujqzY2f7bQtDWxRKZceFC/Djj/Dtt/ZIThLXXWcTSPv29hMsb15Hwww0P/5oL7uIXdDXu7edAZ0/v/vOuXLvSgYuGMjmw5tpU7EN77d/nxrFa7jvhNmk02OVctquXSlJY8kSm0hy54ZmzaB1azvHs149O0iu3GrnTrtkZto0O/CdJ4/trqpa1X3njE+MZ/yG8QxZPISzcWcZ3GAwQ1sOpUCuAu47aRZpolDKm1y8mNLa+P57W4sKbAHDli1t0mjTBqpV0xLpbpSYaBfwzZsHr79u12K88IKdo9Crl83hOb0+4+i5owxZPISJGydSIl8JRrQbQa/avXL2JNmkiUIpb3bokG1l/PCDPZLrTl17bUpro0ULO7tKE4dbPfqorTN17pytHdmzp+2eqlMnZ8+z/sB6Bn07iBsr3sgrrV/J2TfPJk0USvmS3btTksbixfYrLtiiR02b2q+6zZpBrVraVeUG587ZVsZnn9lGX58+tiyYMTaHV6yYM+dJNInEJ8YTFhzG/B3zmfvrXIbdNIz8udw4YJIBTRRK+SpjbNfU8uUpx/799rGCBaFxY5s0mja1az1y53Y2Xj9z/LgdTipTxq65jI62W5706mXXcFxzTc6c552V7/Dxlo/Z0G8DocGhOfOmWaSJQil/smdPStJYsQJiY+39YWF2QLxhw5RDu6tyzJEjKeszNm2y4xetWtmuqpxYmB+XEEdYcBhn/j5D99nd+W+z/9K0XNOrf2MXaaJQyp8dO2YX+61YAatX23rcyZs4FCtm991IThwNGmhhwxwQGwvTp9sNE1eutDOnPv8czp+3022v5hJvOrSJztM7s+/0Pu6uczdv3/g21+a/NsdiT48mCqUCyaVLtrtqzZqUY/v2lNIiVapAVJRdmVavnv2pyeOqdewICxbYvTVuusluwtSlCxTIxgzYc3HneGPFG7zz0zuEBYcxtMVQBjccTFhwWM4HnkQThVKB7tQp28m+Zo2tVbVxI+zbl/J4+fIpSSM5gVx7rXZbZYExdnfdmTPtsW+fbV18+aV9/OLFrA8h7Tyxk8cWPcY3O76hatGqvN/+fW667qYcjx00USil0nLsmF1ptnGj/fnzz7BjR8rjJUrYpFG7tp1hVbu23TpWa1dlKjHR9gKGhtoB8H377LKYDh1sS6NDh6wtyp+/Yz6PLnqUnSd20rVaV0a0G0GFQhVyNGZNFEop15w5A5s3pySPTZtst9Xff9vHRWx9q1q1/nlUrmw/FVWa9u61xYdnzbKD4vnywS232O3aK1Vy7T3+jv+bEatG8Nry15jXcx6tKrbK0Rg1USilsi8+3ta9iIn55/HbbynV9sLCbA2MatXsz9RHdjrp/VRCgl2U//nn8NVXsGWL3Q9ryRI4fRratcu8e+rEhROXd9J7e+XbVClahVur3XrVsWmiUErlvIsX7W5BqZPHr7/aLWSTEwjYxQZXJo8qVezU3ZAQ5+J3WGJiSomQ226zYxnh4dCpE9xxh60bmVH31KWESzSc2JDoUtGMu2XcVcejiUIp5TlxcbYI4q+//vs4fjzleSEhdhC9UiVbVbdSpX8eBQs69zd42KVLtlUxe7ZNGMeO2Q0Uf/zRPh4XZxttV4pPjOdi/EXCw8JZs38NM2JmMLTlUArlLpTlGDRRKKW8w/HjKUnjt99s6yP5SJ1EAIoW/XfyKF/ebgxVtqzflmiPj7fbmyQkQNu2dtiofHlbL/KOO2yLI63evOE/Deep756iWN5ivN7mdfpG9iU4yPUSL5oolFLe79SpfyaO5GPXLrsaPT7+n88vWtQmjeTEkfx78u1rr/WLWlhHjsCrr8IXX8CBA7Zl0a4dvPyy3YE3tY0HNzL428Gs3LeS+tfWZ1T7UTQq28il82iiUEr5tvh4W+Nq714713Tv3n8e+/bZRJNaSIgtAVu6tE0apUrZI/XvpUrZ8u4+sF4kecrt7Nn2WLDATjhbvdquFO/SxeZOYwzTY6bz1HdPceDMAXrX6c1bN76V6epuTRRKKf936lRKEkmdTA4csMfBg/9OJgC5cqWdRK65xq4lKVnS/ixe3D7XCyR/LIvY0ugjR9rGU+vWcOeddqFfnoJneX356wxfNZyw4DBeaP4CjzR8hFwhaf8NmiiUUgpsDfGDB+2ROoEk/558+/TptF9fsKBNGq4cRYrk/M5HaTDGLntJbmns3GknlO3aZRNJzJ+7GLL8cVbuXcmOQTsuT629kiYKpZTKirNn4fBhO0CQ2XHs2D+nAycLCrI1tIoWzdpxFaXijbFrMw4csNNrExJsifQqVeDGrgfoe0cpri2VwBP/9wQDowdSuWjly6/12kQhIjcDI4FgYKIx5s0rHpekxzsA54E+xpiNGb2nJgqllEclJMCJEzZppE4uR4/amVxpHefPp/9+efOmnUAKF077KFLE/gwP/9dYy7lzMGyYXRGevONu7Ru3sKtFU6Z0nUi3mt0uP/dqEoXbVsOISDAwGmgL7AfWichcY0xsqqe1ByonHQ2BD5N+KqWUdwgOtuMXxYtDzZquvebixfSTyJXHvn32519/2aSUnpAQOzCfKonkK1yYoYULM7RLYX7tUIkvdkbwxebrmHrTV9weV5gtCw/wwqo5NL7h6lbPu3PZZANgpzHmdwARmQF0AVInii7ANGObNatFpJCIXGuMOejGuJRSyr1y506ZkeUqY+yiipMnXT9+/922dv76i6oJCfwX+C/A0/Ytl/Awc+/ZzordJ6/qz3FnoigNpKpzzH7+3VpI6zmlgX8kChHpB/RLuvm3iMTkbKg+qxhwzOkgvIReixR6LVIE+LX4AKbBCXujanbfxZ2JIq2Jy1cOiLjyHIwx44HxACKyPrv9bP5Gr0UKvRYp9Fqk0GuRQkSyPbjrzrld+4GyqW6XAQ5k4zlKKaUc5M5EsQ6oLCIVRSQM6AHMveI5c4F7xLoBOKXjE0op5V3c1vVkjIkXkYeBRdjpsZONMdtEpH/S42OBBdipsTux02P7uvDW490Usi/Sa5FCr0UKvRYp9FqkyPa18LkFd0oppTzL/evPlVJK+TRNFEoppTLktYlCRG4WkV9FZKeIPJvG4yIi7yc9vkVE6jkRpye4cC3uSroGW0TkJxGJcCJOT8jsWqR6XrSIJIjIHZ6Mz5NcuRYi0lJENonINhH50dMxeooL/0YKisg8EdmcdC1cGQ/1OSIyWUSOpLfWLNufm8YYrzuwg9+7gEpAGLAZqHHFczoA32LXYtwArHE6bgevRWOgcNLv7QP5WqR63mLsZIk7nI7bwf8vCmErIZRLul3C6bgdvBb/Bd5K+r04dg1amNOxu+FaNAfqATHpPJ6tz01vbVFcLv9hjIkDkst/pHa5/IcxZjVQSEQy3rnDN2V6LYwxPxljktfor8auR/FHrvx/ATAI+AI44sngPMyVa9ELmGOM2QtgjPHX6+HKtTBA/qRCpOHYRHHFlnq+zxizjMsLsdOUrc9Nb00U6ZX2yOpz/EFW/877sd8Y/FGm10JESgNdgbEejMsJrvx/UQUoLCJLRWSDiNzjseg8y5Vr8QFQHbugdyvwiDEmjdrhfi9bn5vuLOFxNXKs/IcfcPnvFJFW2ETR1K0ROceVa/Ee8IwxJkF8YPvLq+DKtQgB6gNtgDzAKhFZbYzZ4e7gPMyVa9EO2AS0Bq4DvhOR5caYdHYw8lvZ+tz01kSh5T9SuPR3ikgdYCLQ3hhz3EOxeZor1yIKmJGUJIoBHUQk3hjzlUci9BxX/40cM8acA86JyDIgAvC3ROHKtegLvGlsR/1OEdkNVAPWeiZEr5Gtz01v7XrS8h8pMr0WIlIOmAP09sNvi6llei2MMRWNMRWMMRWA2cAAP0wS4Nq/ka+BZiISIiJ5sdWbt3s4Tk9w5VrsxbasEJGS2Eqqv3s0Su+Qrc9Nr2xRGPeV//A5Ll6LF4GiwJikb9Lxxg8rZrp4LQKCK9fCGLNdRBYCW4BE7C6Tflei38X/L14BPhKRrdjul2eMMX5XflxEpgMtgWIish8YCoTC1X1uagkPpZRSGfLWriellFJeQhOFUkqpDGmiUEoplSFNFEoppTKkiUIppVSGNFGogCQikSLSIZ3HokTkfQ/H0zmjarjpvOZsGveVFZElIrI9qUrqIzkXpQpUOj1WBSQR6QNEGWMe9oJYQowxWS5QJyJnjTHhV9x3LXCtMWajiOQHNgC3GmNicyhcFYC0RaF8kojck1RPf7OIfJx0X3kR+SHp/h+SVqwjIneKSEzSc5clrd59GeietFdD9yveu6WIfJP0+/+SavwvFZHfRWRwOvGcFZHhIrIx6dzFk+6/TkQWJhXlWy4i1ZLu/0hERojIEuAtEekjIh9k8ndUFJFVIrJORF5JKw5jzEFjzMak389gV2L7Y7FM5UGaKJTPEZGawBCgtTEmAkjuXvkAW0K5DvApkNx99CLQLum5nZNKUb8IfG6MiTTGfJ7JKathi8o1AIaKSGgaz8kHbDTG1AN+xK6IBbuh/SBjTH3gSWBMqtdUAW40xjxxxXul93eMBD40xkQDhzKJGRGpANQF1mT2XKUyoolC+aLWwOzkEgzGmOT6+42Az5J+/5iUKrorseUbHsSWeMiq+caYv5POdwQomcZzEoHkhPMJ0FREwrGbSs0SkU3AOCB17f9ZxpiENN4rvb+jCTA91f3pSjr3F8CjAVghVeUwr6z1pFQmBNdKyhsAY0x/EWkIdAQ2iUhkFs/3d6rfE3Dt343BfhH7yxiT3vnOuXh+k87vaUpq8XwBfGqMmePiOZRKl7YolC/6AegmIkUBRKRI0v0/YSuHAtwFrEh6/DpjzBpjzIvAMWyZ5TNA/hyMKQhI3p+7F7Ai6Zv8bhG5MykOEdf2M0/z78C2jFLf/y9iq0JOArYbY0Zk+a9QKg2aKJTPMcZsA14DfhSRzUDyB+JgoK+IbAF6kzJ28Y6IbBW74fwy7J7KS4AaaQ1mZ9M5oKaIbMB2jb2cdP9dwP1JcW4j7a1br5Te3/EIMFBE1gEF03ltk6TXtE762zalNw1YKVfp9FilckBaU1WV8hfaolBKKZUhbVEopZTKkLYolFJKZUgThVJKqQxpolBKKZUhTRRKKaUypIlCKaVUhv4fe0c7XIw0PU4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = {}\n",
    "v2 = {}\n",
    "uv2 = {}\n",
    "total_vote = {}\n",
    "vote_share1 = {}\n",
    "\n",
    "eps_list = np.arange(0,1,0.001)\n",
    "beta = 0.9\n",
    "\n",
    "for j in [0.1,0.5,0.9]:\n",
    "    \n",
    "    c1 = j\n",
    "\n",
    "    vote1_list = []\n",
    "    vote2_list = []\n",
    "    uncond_vote2_list = []\n",
    "    \n",
    "    for eps2 in eps_list:\n",
    "        \n",
    "        uvote2 = 1-cdf(eps2)\n",
    "        ee2 = cond_exp(eps2)\n",
    "        \n",
    "        eps1 = epstar1(c1,beta,uvote2,ee2,eps2)\n",
    "        \n",
    "        vote1 = 1-cdf(eps1)\n",
    "        vote1_list.append(vote1)\n",
    "        vote2 = (1-vote1)*uvote2\n",
    "        vote2_list.append(vote2)\n",
    "        uncond_vote2_list.append(uvote2)\n",
    "\n",
    "    v1[str(j)] = np.array(vote1_list)\n",
    "    v2[str(j)] = np.array(vote2_list)\n",
    "    uv2[str(j)] = np.array(uncond_vote2_list)\n",
    "    \n",
    "    total_vote[str(j)] = v1[str(j)] + v2[str(j)]\n",
    "    vote_share1[str(j)] = v1[str(j)] / total_vote[str(j)]\n",
    "\n",
    "vote1 = pd.DataFrame(v1)\n",
    "vote2 = pd.DataFrame(v2)\n",
    "uncond_vote2 = pd.DataFrame(uv2)\n",
    "total_vote = pd.DataFrame(total_vote)\n",
    "vote_share1 = pd.DataFrame(vote_share1)\n",
    "\n",
    "vote1.index = eps_list\n",
    "vote2.index = eps_list\n",
    "uncond_vote2.index = eps_list\n",
    "total_vote.index = eps_list\n",
    "vote_share1.index = eps_list\n",
    "\n",
    "vote_share1.plot.line(style=['r', 'b--', 'g-.'])\n",
    "plt.legend(title='cost in period 1',loc='best')\n",
    "plt.xlim([0.0,1.0])\n",
    "plt.ylim([0.0,1.0])\n",
    "plt.xlabel('cost in period 2')\n",
    "plt.ylabel('turnout share of period 1')\n",
    "#plt.savefig('vote_share1.png') \n",
    "plt.show()\n",
    "\n",
    "vote1.plot.line(style=['r', 'b--', 'g-.'])\n",
    "plt.legend(title='cost in period 1',loc='best')\n",
    "plt.xlim([0.0,1.0])\n",
    "plt.ylim([0.0,1.0])\n",
    "plt.xlabel('cost in period 2')\n",
    "plt.ylabel('turnout in period 1')\n",
    "#plt.savefig('vote1.png') \n",
    "plt.show()\n",
    "\n",
    "vote2.plot.line(style=['r', 'b--', 'g-.'])\n",
    "plt.legend(title='cost in period 1',loc='best')\n",
    "plt.xlim([0.0,1.0])\n",
    "plt.ylim([0.0,1.0])\n",
    "plt.xlabel('cost in period 2')\n",
    "plt.ylabel('turnout in period 2')\n",
    "#plt.savefig('vote2.png') \n",
    "plt.show()\n",
    "\n",
    "total_vote.plot.line(style=['r', 'b--', 'g-.'])\n",
    "plt.legend(title='cost in period 1',loc='best')\n",
    "plt.xlim([0.0,1.0])\n",
    "plt.ylim([0.0,1.0])\n",
    "plt.xlabel('cost in period 2')\n",
    "plt.ylabel('overall turnout')\n",
    "#plt.savefig('total_vote.png') \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = {}\n",
    "v2 = {}\n",
    "\n",
    "eps_list = np.arange(0,1,0.001)\n",
    "beta = 0.9\n",
    "\n",
    "for j in [0.1,0.2]:\n",
    "    \n",
    "    c1 = j\n",
    "\n",
    "    foc1_list = []\n",
    "    foc2_list = []\n",
    "    uncond_vote2_list = []\n",
    "    \n",
    "    for eps2 in eps_list:\n",
    "        \n",
    "        uvote2 = 1-cdf(eps2)\n",
    "        foc1 = beta*(1-cdf(eps2))\n",
    "\n",
    "        ee2 = cond_exp(eps2)\n",
    "        eps1 = epstar1(c1,beta,uvote2,ee2,eps2)\n",
    "        \n",
    "        foc2 = beta*((1-cdf(eps2))**2) + cdf(eps1)\n",
    "                     \n",
    "        foc1_list.append(foc1)\n",
    "        foc2_list.append(foc2)\n",
    "        \n",
    "    v1[str(j)] = np.array(foc1_list)\n",
    "    v2[str(j)] = np.array(foc2_list)\n",
    "    \n",
    "df_v1 = pd.DataFrame(v1)\n",
    "df_v2 = pd.DataFrame(v2)\n",
    "\n",
    "df_v1.index = eps_list\n",
    "df_v2.index = eps_list\n",
    "\n",
    "df = pd.concat([df_v1, df_v2], axis=1)\n",
    "\n",
    "df.plot.line(style=['r', 'b--','r', 'b--'])\n",
    "handles, labels = plt.gca().get_legend_handles_labels()\n",
    "by_label = dict(zip(labels, handles))\n",
    "plt.legend(by_label.values(), by_label.keys(),title='cost in period 1',loc='best')\n",
    "plt.xlim([0.0,1.0])\n",
    "plt.ylim([0.0,0.8])\n",
    "plt.xlabel('cost in period 2')\n",
    "#plt.savefig('focs.png') \n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
